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Abstract:

We present a novel method for classifying two-dimensional orbits in rotating bar potentials based on an empirical proxy for the second integral of motion, calibrated angular momentum (CAM), which is defined as the ratio of the time-averaged angular momentum ( Lz¯ ) to its temporal dispersion ( σLz ) in the corotating frame. We show that CAM is determined by the ratio of the azimuthal to radial actions ( Jϕ′/Jr′ ) in the analytical Freeman bar model. We then construct a new parameter space defined by CAM versus the rms radius (Rrms) and apply this framework to orbits in several representative rotating bar potentials. In the CAM–Rrms plane, periodic orbits generate well-defined branches separating distinct regions corresponding to different orbital families. Several of these branches enclose isolated areas that can be associated with specific orbital families, such as the x2 orbital family. We further validate the method using orbits from test-particle simulations, which show a well-ordered and nonoverlapping distribution of orbital families in the CAM–Rrms plane. Since CAM is fundamentally linked to intrinsic orbital properties and readily applied to three-dimensional orbits in N-body simulations, our results establish the CAM–Rrms plane as a robust and efficient framework for orbit classification in rotating bars that complements conventional methods.

Abstract:

The Sun is located close to the Galactic mid-plane, meaning that we observe the Galaxy through significant quantities of dust. Moreover, the vast majority of the Galaxy’s stars also lie in the disc, meaning that dust has an enormous impact on the massive astrometric, photometric and spectroscopic surveys of the Galaxy that are currently underway. To exploit the data from these surveys we require good three-dimensional maps of the Galaxy’s dust. We present a new method for making such maps in which we form the best linear unbiased predictor of the extinction at an arbitrary point based on the extinctions for a set of observed stars. This method allows us to avoid the artificial inhomogeneities (so-called ‘fingers of God’) and resolution limits that are characteristic of many published dust maps. Moreover, it requires minimal assumptions about the statistical properties of the interstellar medium. In fact, we require only a model of the first and second moments of the dust density field. The method is suitable for use with directly measured extinctions, such as those provided by the Rayleigh–Jeans colour excess method, and inferred extinctions, such as those provided by hierarchical Bayesian models like StarHorse. We test our method by mapping dust in the region of the giant molecular cloud Orion A. Our results indicate a foreground dust cloud at a distance of 350 pc, which has been identified in work by another author.